PRINCIPLES OF FLIGHT

CONTENT
• Objective
• Chapter 1: Aerodynamics
• Chapter 2: The Four Forces
• Chapter 3: Stability and Control
• Chapter 4: Trimming Controls
• Chapter 5: Flaps and Slats
• Chapter 6: The Stall
• Chapter 7: The Spin Avoidance
• Chapter 8: Load Factor and Maneuvering Flight
• Chapter 9: The Propeller
• VTC SUBJECT EXAM

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 The trainee will have a
OBJECTIVE basic understanding of:
 Aerodynamics
 Load Factor
 Stalling
 The Four Forces
 Flight Controls
 Effects of Weight
 Stall and Spin
Characteristics of
typical light training
aircrafts

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 Chapter 1: Aerodynamics
• Introduction:
o In this subject, aimed at the pilot rather than the scientist, the objective is to
produce a practical guide to the forces that govern aeroplane flight.
o In the first part of the lesson, we will look at some units of measurement,
laws and definitions before moving on to the four forces acting on the
aeroplane in flight and the fundamental principles of how an aerofoil
creates lift

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 Chapter 1: Aerodynamics
• Laws, Definitions and Units of Measurement:
o Units of Measurement:
 Mass is defined as the amount of matter something consists of.
 Weight is the force felt by that amount of matter in normal gravity, an acceleration
of 1g.

Common System International (SI) Units of Measurement

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 Chapter 1: Aerodynamics
• Physical Laws:
o Newton’s 1st Law:
 It states that a body will continue in a state of rest or uniform motion unless acted
upon by an external force.
o Newton’s 2nd Law:
 It states that the rate of change of momentum of a body is proportional to the
applied force and takes place in the direction in which the force acts
o Newton’s 3rd Law:
 It states that to every action there is an equal and opposite reaction.

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• Air in Motion:
o Dynamic Pressure:
 Air behaves in much the same way
irrespective of whether something moves
through the air or the air moves past
something. So the behavior of air in a wind
tunnel (where air is blown past a stationary
shape) is the same as the behavior of air
around a moving object.
 Even the tube is at rest, the tube is
experiencing a pressure from the air around
it. This is known as the static pressure
 Let’s move the tube at 100 knots. There is
an additional pressure caused by the
movement of the tube through the air. This
pressure is known as the dynamic pressure

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• Motion of Air Through a Venturi:
o One of the properties of air in motion is that total pressure is constant. So,
if dynamic pressure is increased, static pressure decreases.

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• Bernoulli’s Theorem:
o It states that an increase in the speed of a fluid occurs simultaneously
with a decrease in static pressure or a decrease in the fluid’s potential
energy.

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• Air Density and Altitude:
o The density is the amount of matter contained in a given volume.
o At low levels, the atmospheric pressure is high and, therefore, so is
atmospheric density. At high level, both atmospheric pressure and
atmospheric density are low. The fall in temperature as altitude increases
only affects the rate at which pressure and density fall
o Air containing water vapor is less dense than dry air and cold air is denser
than warn air at the same height, hence a wing will generate more lift in
cold dry air than warm wet air

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• The Four Forces:
o A pilot needs to know more about lift, how it is created, and how lift
interacts with the other forces acting on an aircraft. Based on Bernoulli’s
theorem, the next chapter investigates the four forces acting on an aircraft
in flight

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 Chapter 2: The Four Forces
• The Four Forces Acting on an
Aircraft in Flight:
o There are four main forces that act
on an aircraft in flight:
 The Weight of the aircraft acting
straight down towards the center of earth
 Thrust, provided by the engine turning
a propeller, acting at approximately 90°
to the plane of rotation of the propeller
 Lift, generated by the airflow around the
wings and acting at approximately 90°
to the airflow meeting the wings.
 Drag, or resistance to the movement of
an object through the air acting behind
the aircraft along its flight path

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• The Four Forces – The Equilibrium State:
o If the aircraft is in straight and level flight at a constant airspeed:
Lift = Weight and Thrust = Drag

o Lift acts through the center of

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• Weight:
o In the world of heavier-than-air flying, aircraft have weight, and every gram or
ounce of that weight has to be supported by lift (and at times some thrust) for an
aircraft to fly.
o Weight (the force of gravity) acts directly towards the center of the earth. It is
considered to act through a point on the aircraft called the center of gravity.
o Clearly, an aircraft designer will work hard to make an aircraft as light as possible.
On one hand, the greater the maximum permitted weight, the more scope the
designer has to provide for payload such as passengers, baggage and fuel, and also
for matter such as structural strength. On the other hand, increasing aircraft weight
reduces performance – meaning longer take-off and landing distances, slower
cruising speeds, reduced range and so on.

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• Wing Loading:
o In level flight, the aircraft’s weight is borne by
lift produced from the wing so a heavier aircraft
requires more lift to maintain level flight than a
lighter one.
o One way to produce more lift is to increase the
wing area; a bigger wing can produce more lift
than a smaller wing of the same shape.
o The ratio between the aircraft weight and wing
area is called the wing loading, and it is simply
aircraft weight divided by wing area.
o The significance of wing loading is that an
aircraft with high wing loading will have to
produce more lift per square foot or square
meter of wing than an aircraft with a low wing
loading

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• Examples of Aircraft Wing Loading:
Piper Vagabond 7.8 lb/sq ft
(two-seat tourer, 80 kts cruise)
Grob 109B 9.2 lb/sq ft
(two-seat motor glider, 90 kts cruise)
Cessna 152 10.5 lb/sq ft
(two-seat trainer, 90 kts cruise)
Cessna 172 13.8 lb/sq ft
(four-seat fixed-undercarriage trainer/tourer, 105 kts cruise)
Beech Bonanza A36 20.2 lb/sq ft
(six-seat retractable-undercarriage, 175 kts cruise)
Learjet 60a 87.3 lb/sq ft
(10-seat twin-jet engines, 450 kts cruise)

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• Thrust:
o Thrust is the force provided by the engine, through the propeller still used on most
General Aviation (GA) aircraft.
o The principle of the principle is that it accelerates a mass of air. This creates a fast-
moving slipstream behind the propeller which can be felt behind an aircraft with its
engine running.
o In fact, a propeller works much like a wing, producing an aerodynamic force when it
is rotating, which in this instance is called thrust

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• Lift:
o The viscosity of air is essential in the
production of lift because there is a point in
carefully optimizing the shape of a wing if the
air will not follow its contour.
o Most parts of the aeroplane contribute to lift in
some way but it is the wings that contribute
the most.
o When the air is slowed down the pressure
increases, and there are two points where it is
stationary, known and the leading and
trailing edge stagnation points, these are
areas of high pressure
• Lift Force acting on a Wing:
o The airflow above the forward part of its section acts very much like the airflow
through the constriction of a venturi. This implies airspeed, increased dynamic
pressure and reduced static pressure.
o Increased airspeed means increased dynamic pressure and so increased lift;
reduced airspeed means reduced lift.
o Lift is greatest where the airflow speed is fastest over the wing, and acts at around
90° to the airflow

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• Angle of Attack (AoA):
o The “angle of attack”, normally referred to as alpha (α ) is the angle between the
relative airflow and the chord line. The chord line is straight line drawn from the
front of the aerofoil to the back

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• Movement of the Center of Pressure:
o At the stalling angle of attack, there is
significant airflow separation from the wing and
a marked loss of lift occurs.
o The distribution of lift across the wing varies
with angle of attack. The point at which total lift
can be said to be acting on aerofoil section is
called center of pressure

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• Drag:
o Drag is defined as the resistance to movement through the air.
 Parasite Drag: the drag that comes from the airflow over the aircraft
 Induced Drag: a by-product of creating lift. It is sometimes called drug drag or
lift dependent drag, which more clearly indicates that the amount of induced
drag we generate depends on how much lift we are creating
 Friction Drag: will occur where the airflow is in direct contact with resist the
movement of the object through the air and slow down the speed of the flow of
the air molecules in direct contact with the surface

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• Ground Effect:
o On take-off and landing, we will encounter ground effect, when the runway surface
suppresses downwash because the air has nowhere to go.
o During landing lift will increase and induced drag will decrease giving the aeroplane
a tendency to float, which may affect the landing distance required
o During take-off, the reverse will occur as we climb out of ground effect, the lift will
decrease and the induced drag will increase

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 Chapter 3: Stability and Control
• Stability:
o “The tendency of an aircraft, when disturbed from a condition of steady
flight, to return to that condition when left to itself” (the late Jeffrey Quill,
test pilot for the Spitfire). This broad definition of stability can be looked at
as two elements – static stability and dynamic stability
 Static stability is a measure of how readily the aircraft tends to return back
towards its original condition

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• Stability (cont.):
 Dynamic stability governs the behavior of the aircraft after the initial static
stability response has started returning it towards the original condition
 It would be good if dynamic stability stopped the restoring motion as soon as
the aircraft returned to its original position, but what is more likely is that
dynamic stability will “dampen” the effect of static stability.

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• The Three Planes of Movement:
o Longitudinal axis: runs through the aircraft from nose to tail
o Lateral axis: runs through the aircraft from wingtip to wingtip
o Normal (or vertical) axis: runs vertically through the aircraft
Movement around these axes are known as:
o Pitching: around the lateral axis
o Rolling: around the longitudinal axis
o Yawing: around the normal (or vertical axis)

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• Stability in Pitch:
o Stability in the pitching sense is known as longitudinal stability, and it is
this which is usually of most concern to designers and pilots alike.
o Stability in pitch is achieved by an appropriate arrangement of the lift and
weight forces acting on the wing, and on the aircraft as a whole.
o An ‘average’ wing is, in isolation, unstable. If disturbed from a particular
angle of attack it will continue to diverge away from it

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• Stability in Pitch (cont.):
o To achieve stability in pitch, the
usual solution is to place a
horizontal tail surface – in effect a
smaller wing – some distance
behind the main wing.
o The change of lift at the wing is
destabilizing, but the change of lift
at the tail is stabilizing because it
will tend to restore the wing to its
original angle of attack

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• Aerodynamic Center (AC) and Center of Gravity (CoG)
o Any aerofoil, such as a wing, possesses a point known as its aerodynamic
center (AC), it is a fixed position regardless of angle of attack and it is
usually very close to one-quarter of the chord back from the aerofoil
leading edge
o The center of gravity (CoG) is the point where the aircraft would balance if
you put a pivot under it
• Control in Pitch
o The conventional method of providing an aircraft with control in pitch is to
hinge part of the horizontal tail so that the rear part can be moved up and
down. This alters the overall camber of the tail surface and thus the amount
of lift (up or down) will produce.
o The part of the horizontal tail that moves up and down is called the elevator

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• Control in Roll
o Control in roll is provided by ailerons, fitted at the outboard trailing edge of
each wing. These move up and down in opposition, thus altering the camber
of that section of each wing and so the amount of lift (and drag) being
produced at each wing.
The primary effect of the aileron is roll
The secondary effect of using aileron is yaw

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• Control in Yaw
o The rear of the vertical tail is hinged in a similar way to the horizontal tail,
and the control surface thus formed is called the rudder. This alters the
camber of the fin/rudder combination and generates lift, which acts to rotate
the rear of the aircraft to the right about its CG
The primary effect of the rudder is yaw
The secondary effect of using aileron is roll

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• Stability in Yaw
o Stability in yaw (normal stability)
is achieved mostly through the fin
(known as the vertical stabilizer)
o Lift is created (in a horizontal
plane) and the aircraft yaws
around the CG until the fin is
meeting the airflow head-on

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 Chapter 4: Trimming Controls
• Introduction:
o Being able to fly without constantly having to hold the control is possibly
the single most important skill to learn as a student pilot and is not always
emphasized during flight instruction
o Without trimming hand flying visually in VMC is made far more difficult
and tiring and hand flying by sole reference to instruments in IMC for any
appreciable length of time is impossible
• Aerodynamic Balance of the Flying Controls:
o The pilot should be able to move the flying controls in flight without having
to use unreasonable effort, but at the same time the controls must not be so
“light” that the pilot could inadvertently overstress the aircraft with a
careless movement of the control column
o To this end the designer will “balance” the flying controls, to provide both
ease of movement and progressive “feel”.
o The generally accepted ideal ratio of control forces is:
 Aileron: 1
 Elevator: 2
 Rudder: 4

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• Trimming Controls:
o Purpose and function:
 Sometimes, it is necessary to apply a constant force to the flying controls ,
flying would soon become very tiring. To alleviate such control forces, some or
all of the flying controls may be fitted with a pilot-adjustable trimmer
 A trimmer usually takes the form of a small control surface (a trim tab) fitted to
the trailing edge of the flying control surface.
 For a control surface that will need regular in-flight trimming, the trim tab is
controlled independently of the flying control by a trim wheel or lever in the
cockpit
• Trimming Controls (cont.):
o Operation:
 In light aircraft, a pilot-controlled trim tab is most often found on the elevator.
 In practice, the pilot only has to do two things:
 Select the airspeed required
 Move the trim control until no pulling or pushing pressure is needed on the control
column to maintain that airspeed
 If a constant push force is required, the trim wheel in the cockpit is would
forward until the push force disappears
 If a constant pull force is required, the trim wheel in the cockpit is wound
back to remove the force
 Once an aircraft is in trim, it will now maintain the desired angle of attack
without the pilot having to maintain a constant pressure on the control column

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 Chapter 5: Flaps and Slats
• The Flaps:
o On a light aeroplane, flaps are sections of the trailing edge of the wing that
can be move and deflected downwards to alter the camber of the wing and
the wing chord line and thus increase the local angle of attack (α). This
increases the coefficient of lift (CL) and thus more lift is created at the same
airspeed
o Generally, the initial flap deflection (10° - 15°) causes a useful increase in
lift for a modest increase in drag. As flap is deflected further, lift increases
at a lesser rate but drag becomes much more significant
• The Slaps, Slots and Air Brakes:
o Slats and slots along the front section of the wings are known as Leading
Edge Devices.
 A slot is a fixed gap in the leading of the wing.
 A section of leading edge that moves in and out is called a slat
o A slat or slot in the leading edge increases lift close to the stall by allowing
relatively high-pressure air from just underneath the wing to flow over the
wing’s upper surface, re-energizing the airflow and delaying airflow
separation.
o Gliders, motor gliders and certain light aircraft are fitted with airbrakes,
whose only function is to increase drag
• The Spoilers:
o Spoilers are sections of the upper
wing surface that can be deflected
to reduce lift (and increase drag)
on the wing. When used
symmetrically, spoilers act as a
type of airbrake or ‘speed brakes’.
High speed aircraft can also use
spoilers asymmetrically for roll
control
o Spoilers are often favored for
high-speed aircraft because in this
regime of flight, spoilers are a
more effective means of roll
control than ailerons

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 Chapter 6: The Stall
• The Boundary Layer:
o The Laminar Flow is the smooth Boundary Layer, only a few millimeters
thick, and within which there is no vertical movement of the air molecule;
that is to say
o The Turbulent Layer is a thick chaotic Boundary Layer, ten times thicker
than the laminar layer.
o The point at which laminar flow changes to turbulent flow is called
transition point

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• Airflow Separation:
o Further aft of the transition point the boundary layer breaks down and
separates from the surface leaving a wake of random and disturbed flow
called separated airflow
o The point where separation occurs is called the separation point

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• Effect of Increasing AoA on CL and CD:
o Since lift is only generated in regions of laminar flow it stands to reason
that as the angle of attack increases and the separation point moves forward
there will be a smaller and smaller area of laminar flow and the point will
come where the coefficient of lift will increase no further and further
increases of the angle of attack will result in a decrease in lift. This is called
the critical angle of attack or critical alpha
o the separated flow will also cause a sharp increase in induced drag (and
therefore coefficient of Drag) up to and beyond critical alpha
• Stalling Airspeed:
o Because light aircraft do not
usually have an angle-of-attack
indicator, airspeed is the primary
reference for avoiding the stall
o The specified circumstances in
the case of :
 Vs0 (bottom of white arc on
airspeed indicator): Wings
Level, Power Off, Maximum
Gross Weight, Flaps fully down
 Vs1 (bottom of green arc on
airspeed indicator): Wings
Level, Power Off, Maximum
Gross Weight, Flaps fully up
• Factors Affecting Stalling Airspeed:
o Weight:
 The heavier the aircraft, the greater the angle of attack required at any particular
airspeed to produce the same amount of lift, so the stalling angle of attack is
reached at a higher airspeed than for a less heavy aircraft
o Load Factor:
 Increased load factor leads to increased stalling airspeed
o Angle of bank:
 The steeper the angle of bank in a level turn, the higher the load factor and so
the higher the stalling airspeed
o Power:
 The more power is used, the slower the stalling airspeed
o Flaps:
 Flaps increase the maximum CL the wing can produce, meaning that the aircraft
can fly more slowly before running out of lift
• Factors Affecting Stalling Airspeed (cont.):
o Center of Gravity:
 A forward CoG increases the stalling airspeed.

Increased Decreased
Weight Higher stalling airspeed Slower stalling airspeed
Load Factor Higher stalling airspeed Slower stalling airspeed
Angle of Bank Higher stalling airspeed Slower stalling airspeed
Power Slower stalling airspeed Higher stalling airspeed
Flaps Slower stalling airspeed Higher stalling airspeed
CoG Rearwards Slower stalling airspeed
CoG Forwards Higher stalling airspeed
• Symptom of the Stall:
o The classic symptoms of an approaching stall, not all of which may
manifest themselves in every stall, are:
 Control column well back.
 Abnormally slow airspeed for the maneuvers being flown, airspeed reducing
further
 Unusually nose-high attitude for the maneuvers being flown
 “sloppy” and ineffective flying controls
 Unusual quietness
 Stall warner operating
 High rate of descent
 “Buffet” of the airframe as airflow detaches from the wing
 Possible wing drop
 Chapter 7: Spin Avoidance
• Causes of a Spin:
o A spin occurs when an aircraft stalls within significant yaw present, and the
consequent wing drop allows the aircraft to develop autorotation.
o Autorotation in a fixed-wing aircraft is a condition where the aircraft is
rotating of its own accord, without further control input from the pilot.
• Direction of a Spin:
o An often under-appreciated point is that if an aircraft does spin, it will do so
in the direction of any rudder applied at the stall. Thus, if a pilot stalls an
aircraft with left rudder applied, any resulting spin will be to the left
• Stall before Spin:
o In a spin, the aircraft will be
descending vertically (a rate of
decent of 6000fpm is quite
common, even in a light aircraft),
yawing at an impressive rate (a
complete turn every few seconds or
so) and probably also pitching and
rolling through each turn.
o An aircraft has to stall before it can
spin. Prevent the stall and you
prevent the spin
• The Forces in a Spin:
o The traditional arrangement of forces in ‘normal’ flight conditions are
somewhat altered in a spin. Indeed, they are augmented by the gyroscopic
force, which acts so that a large mass at the extremities of the aircraft tends
to lead a flatter spin. Generally, the flatter the spin, the more difficult and
prolonged the recovery.
o An aircraft with a long wing span compared to the fuselage length will
tend to have a slower rate of rotation in the spin than one with a shorter
relative wing span
• Spin Recovery:
o Because of the height loss involved in a spin and recovery, timely
recognition of a spin and correct recovery action is essential. Although the
spin is a stalled condition, the recovery actions are different from those of a
standard stall recovery.
o The standard spin-recovery procedure:
 Check throttle closed and ailerons neutral (flaps up)
 Confirm direction of spin, apply full opposite rudder
 Move the control column forward until rotation stops; and
 Centralize the rudder and recover from the ensuing dive
• Spin Direction and Further Recovery Actions:
o It is normally possible to see the spin direction by looking ahead, although
the turn indicator or turn coordinator should accurately show the direction
of the spin too. Ignore indications from the balance ball
• The Spiral Dive:
o If the spin entry does not go correctly, the
aircraft may well end up in a spiral dive.
As the name implies, this is basically a
steep descending spiral rather than the
vertical, rotating descent of the spin.
o A rapidly increasing airspeed indicates a
spiral dive while steady airspeed around
the stall indicates a spin
o an aircraft can normally be recovered from
a spiral dive by:
 Levelling the wings with aileron and
recovering gently from the dive
 Reducing power during the pull-out will
reduce load factor on the aircraft
 Chapter 8: Load Factor in Flight
• Straight Horizontal Steady Flight:
o In level flight, the forces of lift/weight and thrust/drag are in equilibrium
and are accompanied by coupling actions trying to pitch the aeroplane nose
down and nose up respectively
• Straight Steady Climb:
o During Climb, weight continues
to act vertically downwards but
now the lift force is no longer
directly aligned with weight,
because lift acts at right angles to
the flight path, not horizontal. Lift
is only required to balance the
slightly smaller component of
weight shown by the light green
dotted line.
o The other component of weight
acts parallel to the flight path in
the same direction as
aerodynamic drag and is referred
as weight apparent drag
• Straight Steady Descent:
o The forces in a powered descent are, thankfully, very similar to those in the
climb. The only difference is the component of weight that resulted in
weight apparent drag is now helping to propel the aeroplane down the slope
and is called weight apparent thrust
• Straight Steady Glide:
o The forces acting on an aeroplane in a straight steady glide are all identical
but of course there is no thrust component generated by the propeller but
weight apparent thrust, due to the component of weight acting parallel to
the flight path, is still present
• Straight Coordinated Turn:
o In a turn the total lift (supporting the weight and providing a force to turn
the aeroplane) is greater than the lift in straight and level flight, which only
support the weight. This is felt as we sense an increase in ‘g’ loading as the
load factor increases
• Maneuvering Flight:
o It is in maneuvering flight (e.g. steep turns, pulling out of a dive, a sharp
pull-up into a climb etc.) that the effect of load factor upon the aircraft
becomes much more noticeable
 Chapter 9: Propeller
• Principles of Propeller:
o Stationary Aeroplane:
 A propeller blade can be considered as a
small rotating wing producing lift the
same way a wing does.
 The propeller ‘wing’ is, however,
mounted vertically and is driven by the
engine to produce lift (called thrust) in a
rearward direction
 Consider the stationary aircraft with the
blade set vertically downwards (with
angle of attack (α) of 0°), when turning
no thrust would be generated because no
air is pushed backwards.
 If we now change the angle of attack to
some positive value then air would be
pushed backwards and thrust generated
• Principles of Propeller (cont.):
o Moving Aeroplane:
 At low forward speed α is the angle
between the pink ‘Low Speed” line and
the propeller chord line. As the speed
increase α decreases, as shown by the
orange and red lines. This means a given
throttle setting on a fixed pitch propeller
aeroplane will result in a certain
rotational propeller speed and a certain α
 As the aeroplane speeds up α will
decrease to zero and the aeroplane will
not accelerate anymore. If more power is
applied the rotational speed of the
propeller will increase, the blade speed
will increase and the vertical line in the
plane of rotation will become longer, α
will increase and the aeroplane will
accelerate again
• Blade Twist:
o Since the center of propeller blade rotates around its own axis and thus
has zero vertical speed through the air but the tip of the blade has
significant vertical speed through the air it can be said that the speed of
any part of the blade vertically through the air (in the plane of rotation) is
related to how far that part of the propeller is from the center
o The α changes as the speed of the blade through the air (in the plane of
rotation) changes, thus it follows that we need to change the chord line of
the blade in order to keep α constant, hence propeller blades have a twist
along their own longitudinal axis
• Blade Twist:
o Since the center of propeller blade rotates
around its own axis and thus has zero
vertical speed through the air but the tip
of the blade has significant vertical speed
through the air it can be said that the
speed of any part of the blade vertically
through the air (in the plane of rotation)
is related to how far that part of the
propeller is from the center
o The α changes as the speed of the blade
through the air (in the plane of rotation)
changes, thus it follows that we need to
change the chord line of the blade in
order to keep α constant, hence propeller
blades have a twist along their own
longitudinal axis
• Thrust and Torque Forces:
o The total reaction force on the aerofoil
acts out of the cambered side of the
blade, called the thrust face and is split
into two components. These are thrust
which acts at 90° to the plane rotation,
and propeller torque which is parallel to
the rotational plane.
o Propeller torque normally opposes engine
torque.
o Propeller torque is sometimes referred to
as the drag of the propeller
• Windmilling Propeller:
o An engine failure will mean that power
and torque suddenly stop reaching the
propeller. This does not mean that the
propeller will stop rotating, it will
continue to rotate as the airflow passing
through the blades drive the propeller and
the attached engine, in the same way, a
wind turbine or windmill is driven by the
wind
o A windmilling propeller will result in
high drag, especially if the propeller is
attempting to turn a damaged or seized
engine
• Propeller Icing:
o In conditions where icing is likely,
propeller icing can be very serious, as the
blade is affected by icing in the same way
as a fixed-wing
o Any accumulation will change the
aerodynamic. A fall in efficiency of up to
20% is possible as thrust decreases and
drag increases. It can quickly be
impossible to maintain speed and
altitude.
o In addition, any slight variation in ice
accumulation along the blades will affect
the balance of the propeller causing
severe noise and vibration
 THANK YOU
ANY QUESTION?

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